Also draw graph of Original Budget constraint, new budget constraint, compensated budget constraint

2. (20 Total Points) Suppose a consumer's utility function is given by U(X,Y) = X12+Y12. Also, the consumer has $36 to spend, and the price of Good X, Px = $4. Let Good Y be a "composite" good (Good Y is the "numeraire") whose price is Py = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. a) (2 points) How much X and Y should the consumer purchase in order to maximize her utility? X * = Y* = b) (2 points) How much total utility does the consumer receive? U(X*, Y* ) = c) (2 points) Now suppose Px increases to $9. What is the new bundle of X and Y that the consumer will demand? X* * = Y* * = d) (2 points) How much additional money would the consumer need in order to have the same utility level after the price change as before the price change? (Note: this amount of additional money is called the Compensating Variation.) Compensating Variation = e) (2 points) Of the total change in the quantity demanded of Good X, how much is due to the substitution effect and how much is due to the income effect? (Note: since there is an increase in the price of Good X these values will be negative). SE = IE =